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Register a new userThe blistering of a viscoelastic filament of a droplet of saliva
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A fluid dynamics video of the break up of a droplet of saliva is shown. First a viscoelastic filament is formed and than the blistering of this filament is shown. Finally, a flow induced phase separation takes place nanometer sized solid fiber remains that consist out of the biopolymers.
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When a dilute polymer solution experiences capillary thinning, it forms an almost uniformly cylindrical thread, which we study experimentally. In the last stages of thinning, when polymers have become fully stretched, the filament becomes prone to instabilities, of which we describe two: A novel breathing instability, originating from the edge of the filament, and a sinusoidal instability in the interior, which ultimately gives rise to a blistering pattern of beads on the filament. We describe the linear instability with a spatial resolution of 80 nm in the disturbance amplitude. For sufficiently high polymer concentrations, the filament eventually separates out into a solid phase of entangled polymers, connected by fluid beads. A solid polymer fiber of about 100 nanometer thickness remains, which is essentially permanent.
In this work we consider theoretically the problem of a Newtonian droplet moving in an otherwise quiescent infinite viscoelastic fluid under the influence of an externally applied temperature gradient. The outer fluid is modelled by the Oldroyd-B equation, and the problem is solved for small Weissenberg and Capillary numbers in terms of a double perturbation expansion. We assume microgravity conditions and neglect the convective transport of energy and momentum. We derive expressions for the droplet migration speed and its shape in terms of the properties of both fluids. In the absence of shape deformation, the droplet speed decreases monotonically for sufficiently viscous inner fluids, while for fluids with a smaller inner-to-outer viscosity ratio, the droplet speed first increases and then decreases as a function of the Weissenberg number. For small but finite values of the Capillary number, the droplet speed behaves monotonically as a function of the applied temperature gradient for a fixed ratio of the Capillary and Weissenberg numbers. We demonstrate that this behaviour is related to the polymeric stresses deforming the droplet in the direction of its migration, while the associated changes in its speed are Newtonian in nature, being related to a change in the droplets hydrodynamic resistance and its internal temperature distribution. When compared to the results of numerical simulations, our theory exhibits a good predictive power for sufficiently small values of the Capillary and Weissenberg numbers.
In many macroscopic dynamic wetting problems, it is assumed that the macroscopic interface is quasistatic, and the dissipation appears only in the region close to the contact line. When approaching the moving contact line, a microscopic mechanism is required to regularize the singularity of viscous dissipation. On the other hand, if the characteristic size of a fluidic system is reduced to a range comparable to the microscopic regularization length scale, the assumption that viscous effects are localized near the contact line is no longer justified. In the present work, such microscopic length is the slip length. We investigate the dewetting of a droplet using the boundary element method. Specifically, we solve for the axisymmetric Stokes flow with i) the Navier-slip boundary condition at the solid/liquid boundary, and ii) a time-independent microscopic contact angle at the contact line. The profile evolution is computed for different slip lengths and equilibrium contact angles. When decreasing the slip length, the typical nonsphericity first increases, reaches a maximum at a characteristic slip length $tilde{b}_m$, and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behavior for slip lengths larger or smaller than $tilde{b}_m$. Around $tilde{b}_m$, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: viscous elongational flows for large slip lengths, friction at the substrate for intermediate slip lengths, and viscous shear flows for small slip lengths. Following the transitions between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when the slip length is small compared to the droplet size.
Droplet migration in a Hele--Shaw cell is a fundamental multiphase flow problem which is crucial for many microfluidics applications. We focus on the regime at low capillary number and three-dimensional direct numerical simulations are performed to investigate the problem. In order to reduce the computational cost, an adaptive mesh is employed and high mesh resolution is only used near the interface. Parametric studies are performed on the droplet horizontal radius and the capillary number. For droplets with an horizontal radius larger than half the channel height the droplet overfills the channel and exhibits a pancake shape. A lubrication film is formed between the droplet and the wall and particular attention is paid to the effect of the lubrication film on the droplet velocity. The computed velocity of the pancake droplet is shown to be lower than the average inflow velocity, which is in agreement with experimental measurements. The numerical results show that both the strong shear induced by the lubrication film and the three-dimensional flow structure contribute to the low mobility of the droplet. In this low-migration-velocity scenario the interfacial flow in the droplet reference frame moves toward the rear on the top and reverses direction moving to the front from the two side edges. The velocity of the pancake droplet and the thickness of the lubrication film are observed to decrease with capillary number. The droplet velocity and its dependence on capillary number cannot be captured by the classic Hele--Shaw equations, since the depth-averaged approximation neglects the effect of the lubrication film.
If a droplet is placed on a substrate with a conical shape it spontaneously starts to spread in the direction of a growing fibre radius. We describe this capillary spreading dynamics by developing a lubrication approximation on a cone and by the perturbation method of matched asymptotic expansions. Our results show that the droplet appears to adopt a quasi-static shape and the predictions of the droplet shape and spreading velocity from the two mathematical models are in excellent agreement for a wide range of slip lengths, cone angles and equilibrium contact angles. At the contact line regions, a large pressure gradient is generated by the mismatch between the equilibrium contact angle and the apparent contact angle that maintains the viscous flow. It is the conical shape of the substrate that breaks the front/rear droplet symmetry in terms of the apparent contact angle, which is larger at the thicker part of the cone than that at its thinner part. Consequently, the droplet is predicted to move from the cone tip to its base, consistent with experimental observations.
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